Tight Bounds for Randomized Load Balancing on Arbitrary Network Topologies

We consider the problem of balancing load items (tokens) in networks. Starting with an arbitrary load distribution, we allow nodes to exchange tokens with their neighbors in each round. The goal is to achieve a distribution where all nodes have nearly the same number of tokens. For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains, whose convergence is fairly well-understood in terms of their spectral gap. However, in many applications, load items cannot be divided arbitrarily, and we need to deal with the discrete case where the load is composed of indivisible tokens. This discretization entails a non-linear behavior due to its rounding errors, which makes this analysis much harder than in the continuous case. We investigate several randomized protocols for different communication models in the discrete case. As our main result, we prove that for any regular network in the matching model, all nodes have the same load up to an additive constant in (asymptotically) the same number of rounds as required in the continuous case. This generalizes and tightens the previous best result, which only holds for expander graphs, and demonstrates that there is almost no difference between the discrete and continuous cases. Our results also provide a positive answer to the question of how well discrete load balancing can be approximated by (continuous) Markov chains, which has been posed by many researchers.Comment: 74 pages, 4 figure

Regulating the adaptive immune response to respiratory virus infection

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Recent years have seen several advances in our understanding of immunity to virus infection of the lower respiratory tract, including to influenza virus infection. Here, we review the cellular targets of viruses and the features of the host immune response that are unique to the lungs. We describe the interplay between innate and adaptive immune cells in the induction, expression and control of antiviral immunity, and discuss the impact of the infected lung milieu on moulding the response of antiviral effector T cells. Recent findings on the mechanisms that underlie the increased frequency of severe pulmonary bacterial infections following respiratory virus infection are also discussed

The Fast Heuristic Algorithms and Post-Processing Techniques to Design Large and Low-Cost Communication Networks

It is challenging to design large and low-cost communication networks. In this paper, we formulate this challenge as the prize-collecting Steiner Tree Problem (PCSTP). The objective is to minimize the costs of transmission routes and the disconnected monetary or informational profits. Initially, we note that the PCSTP is MAX SNP-hard. Then, we propose some post-processing techniques to improve suboptimal solutions to PCSTP. Based on these techniques, we propose two fast heuristic algorithms: the first one is a quasilinear time heuristic algorithm that is faster and consumes less memory than other algorithms; and the second one is an improvement of a stateof-the-art polynomial time heuristic algorithm that can find high-quality solutions at a speed that is only inferior to the first one. We demonstrate the competitiveness of our heuristic algorithms by comparing them with the state-of-the-art ones on the largest existing benchmark instances (169 800 vertices and 338 551 edges). Moreover, we generate new instances that are even larger (1 000 000 vertices and 10 000 000 edges) to further demonstrate their advantages in large networks. The state-ofthe-art algorithms are too slow to find high-quality solutions for instances of this size, whereas our new heuristic algorithms can do this in around 6 to 45s on a personal computer. Ultimately, we apply our post-processing techniques to update the bestknown solution for a notoriously difficult benchmark instance to show that they can improve near-optimal solutions to PCSTP. In conclusion, we demonstrate the usefulness of our heuristic algorithms and post-processing techniques for designing large and low-cost communication networks

T Cell Responses during Acute Respiratory Virus Infection

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.The T cell response is an integral and essential part of the host immune response to acute virus infection. Each viral pathogen has unique, frequently nuanced, aspects to its replication, which affects the host response and as a consequence the capacity of the virus to produce disease. There are, however, common features to the T cell response to viruses, which produce acute limited infection. This is true whether virus replication is restricted to a single site, for example, the respiratory tract (RT), CNS etc., or replication is in multiple sites throughout the body. In describing below the acute T cell response to virus infection, we employ acute virus infection of the RT as a convenient model to explore this process of virus infection and the host response. We divide the process into three phases: the induction (initiation) of the response, the expression of antiviral effector activity resulting in virus elimination, and the resolution of inflammation with restoration of tissue homeostasis

AGRICULTURAL POLICY INTERVENTIONS IN DEVELOPING COUNTRIES: MAPPING THE NATURE, DEGREE AND PROGRESS OF REFORMS

Replaced with revised version of paper 07/16/04.International Development,